Reasoning

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Reasoning

• Mental Models and Reasoning
• Typical Reasoning Errors

Solso Chapter 14
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Mental models

• Imagery propositional representation (Philip
  Johnson-Laird)
• Schemata in action naïve theories
• Mental models are spatial, dynamic and concrete

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• Surprisingly inaccurate

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• Participant 1 ...momentum is a force that has
  been exerted and put into the ball... The moving
  object has the force of momentum and since there
  is no force to oppose ... It will continue on...
• Participant 2 ...eventually the horizontal
  force would no longer have an effect, and it
  would be a straight downward motion...
• Participant 3 ...the momentum from the curve
  gives the ball the arc... The force that the ball
  picks up from the curve eventually dissipates and
  it will follow a normal straight line...
• a mover...impresses in a
  moving body a certain impetus or force ... in
  the direction toward which the mover was moving
  the body, either up, or down, or laterally, or
  circularly... But that impetus is continually
  decreased by the resisting air and by the
  gravity...

Buridan, XIVc.
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• Theories of movement similar to prenewtonian
  physics! (impetus theory)
• Momentum (impetus) inside the ball that
  dissipates self-expending or because of other
  forces (e.g., does not dissipate in a vacuum)
• Impetus is gained by pushed but not by carried
  object (plane)
• Mental Models usually work, even if they are
  inaccurate
• Navigation in Micronesia

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• Mental models studied in cog. psych
• devices (Hegarty and Just, 1993),
• electricity (Gentner Gentner, 1983),
• computers (Norman, 1988),
• home heating systems (Kempton, 1986),
• navigation (Hutchins, Tversky),
• ecology (Kempton et al. 1995).
• Methods of studying
• Interviews think aloud protocols patterns of
  answers rt eye-movements patterns of retention
  for new materials in the domain.
• Why study inaccurate models?
• Important for learning processes
• Important for design
• Explain some types of reasoning errors

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Mental Models and Reasoning

• Knowledge -gt transformation of knowledge
• Logical reasoning involves building a mental
  model of the premises (Johnson-Laird)
• Models are concrete

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• All artists are beekeepers
• Some of the beekeepers are chemists
• --------
• Some of the artists are chemists
• Syllogisms are more difficult if there are many
  different mental models fitting the premises
• Models are based on typical (stereotypical)
  situations
• Some models are easier to create

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If a card has a vowel on one side, then it has an
even number on the other side. Select only the
card(s) that need to be turned over to validate
this rule. Wasons selection task
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• Each check over 50 has to be signed by the
  manager. Which check(s) do you have to turn over
  in order to see if the rule is obeyed?

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• Abstract/concrete content
• All A are B
• All C are B
• All A are C
• All Republicans are human
• All Democrats are human
• All Republicans are Democrats

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• Other biases in syllogistic reasoning
• Belief bias
• All of the Frenchmen are wine drinkers.
• Some of the wine drinkers are gourmets.
• Therefore, some of the Frenchmen are gourmets.
• All of the doctors are rich.
• Some of the rich people are bankers.
• Therefore, some of the doctors are bankers.

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• Atmosphere effect the form of the premises of a
  syllogism influences expectations about the form
  of the conclusion
• Conversion error (symmetrical relations) All A
  are B means that All B are A Some A are not
  B Some B are not A

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• Individual differences in reasoning performance
• Evans 2003 dual-system theories of reasoning
• System 1 rapid, parallel, automatic,
  belief-based
• System 2 slow, sequential, conscious,
  logic-based
• Differences in intelligence associated with s2
  functioning
• Less belief-bias in people with higher
  intelligence
• Different brain areas active when responses
  correct and incorrect
• Stanovich West (1998) intelligence predicted
  better performance on abstract version of the
  Wason task

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• Are humans rational?
• Inadequate models, errors in logical thinking...
• Reisberg, 1997 One might draw rather cynical
  conclusions... Human reasoning is fundamentally
  flawed
• Wason, 1983 It could be argued that
  irrationality rather than rationality is the
  norm.

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• Logical reasoning and the ability to cope in
  everyday life
• Heuristics are cost-efficient, allow for fast
  decisions (reasonably accurate)
• Errors are less grave than they seem may stem
  from interpretation problems natural language
  operators (if...then ? if and only if...then or
  ?xor)
• Is math invented or discovered?
• Yes!
• However we do make errors (factors such as
  expertise, explicitly given assumptions or
  motivation do not seem to significantly improve
  performance)

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Rationality

• Probabilistic approach (Chater and Oaksford,
  2001)
• People do not make use of logic-based systems
• They make decisions on the basis of incomplete
  information or too much (redundant) information
• Searching for most useful information
• Often failing to provide a complete
  representation of a problem (Johnson-Laird,
  mental models)
• Bounded rationality, situated in the environment
  
• Simon (1990) Human rational behaviour is shaped
  by a scissors whose two blades are the structure
  of task environments and the computational
  capabilities of the actor.

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Judgement and Decision Making

• Based on inductive reasoning, estimating
  probabilities, also prone to errors (Kahneman
  Tversky)
• Availability heuristic (easier to generate
  examples greater probability)
• Representativeness heuristic
• BBBGGG or BGGBGB
• In a certain hospital 65 boys and 35 girls were
  born in 1 day. Is it more probable in a small or
  a large hospital?
• Conjunction error (belief that the combination of
  2 events is more likely than one of the 2 events
  alone)

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• Linda is 31 years old, single, outspoken and very
  bright. She majored in philosophy. As a student
  she was deeply concerned with issues of
  discrimination and social justice.
• Rank the probabilities
• Linda is a bank teller Linda is a feminist
  Linda is a feminist bank teller

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• Combining probablilities e.g., changing belief
  in the probability of a hypotesis in the light of
  new evidence
• Bayes theorem
• P(E/H)P(H)
• P(H/E) ---------------------
• P(E/H)P(H) P(E/H)P(H)
• If a test to detect a disease whose prevalence is
  1/1000 has a false positive rate of 5, what is
  the chance that a person found to have a positive
  result actually has the disease?

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• Harvard Medical School (staff and students)
• 45 estimated the probability of 95 (neglecting
  base-rate probability)
• 18 gave the correct answer 2
• 50 out of 1000 people will give a misleading
  positive finding (and only 1 in 1000 has a
  disease), thus
• There is 50 times more false positive results
  than true positive results, thus
• There is only a 2 chance that a person testing
  positive has the disease

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• Decision making
• Maximizing utility?
• Loss aversion people are more sensitive to
  potential losses than to potential gains
• Will not bet 20 heads, -10 tails
• Choose 800 for sure over 85 probability of
  1000
• Bounded rationality. Heuristic of satisficing
• Choosing the first option that meets the
  individuals minimum requirements

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Problem solving Generating solutions, selection

• Identifying a problem
• Rarely a topic of cognitive psychology (Gestalt
  problem stems from tension between perception
  and memory)
• Problem representation
• Functional fixedness (Gestalt tendency to
  perceive things in terms of their familiar uses)
• Creativity cognitive activity that results in a
  novel way of viewing a problem overcoming
  functional fixedness, cultural blocks

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• Remote Associations Test (Mednick, 1967)
• Find a logically associated word
• (RED, BRIDGE, ANGRY)
• Divergence Production Test (Guilford, 1967)
• Find possible uses for a comb, a button....
• Geneplore model (generate (based on previous
  knowledge) and explore). Increasing creativity
  generating representations before thinking of
  possible uses for them (Ward et al. 1992)
• Solution as representational change
• Change in representational structure
  (elaboration, constraint relaxation, re-encoding)
  -gt retrieval of appropriate cues from LTM
  (Ohlsson, 1992)
• VI VII I IV III I

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• Choosing strategy
• Means-end analysis
• Note the difference between the current state of
  the problem and the goal state
• Form a subgoal that will reduce the difference
• Select a mental operator that will permit
  attainment of the subgoal
• Hill-climbing considering next step, choosing
  one that brigs you closer to the goal.
• Working backwards starting from the end

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• Progress monitoring (rate of progress)
• Failing progress criterion -gt change of strategy
• Much greater sensitivity to constraint relaxation
  after experience of criterion failure (e.g. 9-dot
  problem)

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Transfer of training

• Positive and negative transfer
• Far and near transfer
• Problem solving by analogy
• In science a computer model of human cognition
  a billiard-ball model of gases, etc.
• Noticing similarities in structure
• Dunckers radiation problem

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• Patient with a malignant tumour in his stomach
  can only be saved by a special kind of ray.
  However ray of suficient strength to destroy the
  tumour will also destroy the healthy tissue,
  whereas a ray that will not harm the healthy
  tissue will be too weak to destroy the tumour.
• 10 correct solutions